Olympiad Test : Geometry - 2 - Class 6 MCQ

The sum of all interior angles of a quadrilateral is always 360°. This is because a quadrilateral has four sides, and the sum of interior angles of any polygon with n sides is given by the formula (n - 2) × 180°. For a quadrilateral, n = 4, so the sum is:
(4 - 2) × 180° = 2 × 180° = 360°.

A trapezium (or trapezoid in some countries) is a quadrilateral that has one and only one pair of parallel sides. The other two sides are non-parallel.

• A kite has two pairs of adjacent sides that are equal in length but no parallel sides.
• A rhombus is a type of parallelogram where all sides are equal and opposite sides are parallel.
• A parallelogram has two pairs of parallel sides.

Thus, the correct answer is Option C: A trapezium.

Let the diagram of the triangle ABC be,

From this we can say that there are three sides AB, BC and CA. And there are three angles ∠A, ∠B and ∠C in a triangle.
The total parts of a triangle are the sum of the sides and angles of the triangle.
The total parts of the triangle are 3 + 3 = 6.
So the correct option is C.

Here,
2x + 3x + 4x = 180°

Smallest angle = 2x = 2 × 20° = 40°  

Vertical angle = 180° – (65° + 65°)
= 180° – 130° = 50° 

We know that,

• in an equilateral triangle, all sides are equal
• angles opposite to equal sides are equal
• sum of all angles of a triangle is 180^∘

Hence, all the angles in an equilateral triangle must be equal and the measure of each angle must be equal to 60^∘.

An angle measuring 360° is called a complete angle. This is because a complete angle represents one full rotation, covering the entire circle (360°).

• A straight angle measures 180°, forming a straight line.
• An obtuse angle measures greater than 90° but less than 180°.
• A reflex angle measures greater than 180° but less than 360°.

Thus, the correct answer is Option B: A complete angle.

A straight angle measures 180°. It is formed when the two arms of the angle are in exactly opposite directions, forming a straight line.

• 60° is an acute angle.
• 90° is a right angle.
• 360° is a complete angle.

Thus, the correct answer is Option C: 180°.

An angle measuring 205° is a reflex angle. Reflex angles are those that are greater than 180° but less than 360°.

• An acute angle is less than 90°.
• An obtuse angle is between 90° and 180°.
• A reflex angle is between 180° and 360°.

Thus, the correct answer is Option C: A reflex angle.

The minimum number of points of intersection of three lines in a plane is 0. This happens when all three lines are parallel to each other and do not intersect at any point.

• If the lines are not parallel and intersect, they will meet at at least one point.
• If the lines are concurrent (all meeting at the same point), the number of intersections can be 1.
• If the lines are not concurrent but intersect pairwise, they can intersect at more points, but the minimum number is 0 (when they are parallel).

Thus, the correct answer is Option A: 0.

Two planes intersect in a line. When two planes in three-dimensional space intersect, they always form a straight line along their intersection. They do not intersect at just a point, unless they are identical, and they do not intersect in a plane.

Thus, the correct answer is Option C: In a line.

Other angle = 180° – (90° + 55°)
= 180° – 145° = 35° 

A triangle with sides of different lengths is called a scalene triangle. In a scalene triangle, all three sides have different lengths, and all three angles have different measures.

• A right triangle has one angle that measures exactly 90°.
• An isosceles triangle has two sides of equal length.
• An equilateral triangle has all three sides of equal length.

Thus, the correct answer is Option A: A scalene triangle.

3x + 4x + 5x + 6x = 360°

∴ Largest angle = 6 × 20° = 120°  

A quadrilateral with two pairs of equal adjacent sides but unequal opposite sides is called a kite. In a kite, two pairs of adjacent sides are of equal length, but the opposite sides are not equal. Additionally, the diagonals of a kite intersect at right angles, and one diagonal bisects the other.

• A square has all sides equal and all angles equal to 90°.
• A rectangle has opposite sides equal and all angles 90°.
• A trapezium has only one pair of parallel sides.

Thus, the correct answer is Option B: Kite.

A cone has 1 vertex. The vertex of a cone is the tip or apex, where the sides of the cone meet. The base of the cone is a circular surface, and the vertex is the point opposite to the base.

• A cone does not have multiple vertices like a pyramid (which has a vertex at the top and another at the base).

Thus, the correct answer is Option A: 1.

A brick is an example of a cuboid. A cuboid is a 3D shape with six rectangular faces, and a brick typically has the shape of a rectangular box.

• A cube is a special type of cuboid where all sides are equal in length.
• A prism is a 3D shape with two parallel, congruent polygonal bases and rectangular sides connecting them.
• A cylinder has two circular faces and a curved surface.

Thus, the correct answer is Option D: Cuboid.

A cylinder has 0 vertices. Vertices are points where edges meet, but a cylinder has curved edges and no sharp corners, so it does not have any vertices.

• A cylinder has two circular faces (top and bottom), but no vertices where edges meet.

Thus, the correct answer is Option A: 0.